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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2004 • Question 5

Question

Math 6420 • PDE Fall 2004 • Question 5

Construct the Green’s function for the equation \[ u''(x)+\alpha ^2u(x)=f(x),\qquad u(0)=u(1),\qquad u'(0)=u'(1) \] and express the solution in terms of the Green’s function. For what values of \(\alpha \) does the Green’s function fail to exist?

Raw LaTeX

Construct the Green's function for the equation
\[
  u''(x)+\alpha^2u(x)=f(x),\qquad u(0)=u(1),\qquad u'(0)=u'(1)
\]
and express the solution in terms of the Green's function. For what values of \(\alpha\) does
the Green's function fail to exist?

Topic Tags

Distributions and Weak Solutions Entropy Solutions, Shocks, and Rarefactions Fundamental Solutions Linear Programming and Optimization